The second-order accuracy difference schemes for integral-type time-nonlocal parabolic problems

Allaberen Ashyralyev, Charyyar Ashyralyyev

Contemporary Mathematics Fundamental Directions, 2023

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DOI 10.22363/2413-3639-2023-69-1-32-49

Data confidence 70 medium

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Abstract

This is a discussion on the second-order accuracy difference schemes for approximate solution of the integral-type time-nonlocal parabolic problems. The theorems on the stability of r-modified Crank-Nicolson difference schemes and second-order accuracy implicit difference scheme for approximate solution of the integral-type time-nonlocal parabolic problems in a Hilbert space with self-adjoint positive definite operator are established. In practice, stability estimates for the solutions of the second-order accuracy in t difference schemes for the one and multidimensional time-nonlocal parabolic problems are obtained. Numerical results are given.